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CONSTRUCTIONS BY RULER AND COMPASS, TOGETHER WITH A FIXED CONIC

Published online by Cambridge University Press:  08 March 2013

SEUNGJIN BAEK
Affiliation:
Seoul Science High School, Uamgil 63 (Hyewha-dong 1-1), Jongro-ku, Seoul 110-530, Korea email bjh7790@naver.comyoonhoim@nate.comdwleeid@naver.comsjgceo@naver.com
INSONG CHOE*
Affiliation:
Department of Mathematics, Konkuk University, 1 Hwayang-dong, Gwangjin-Gu, Seoul 143-701, Korea
YOONHO JUNG
Affiliation:
Seoul Science High School, Uamgil 63 (Hyewha-dong 1-1), Jongro-ku, Seoul 110-530, Korea email bjh7790@naver.comyoonhoim@nate.comdwleeid@naver.comsjgceo@naver.com
DONGWOOK LEE
Affiliation:
Seoul Science High School, Uamgil 63 (Hyewha-dong 1-1), Jongro-ku, Seoul 110-530, Korea email bjh7790@naver.comyoonhoim@nate.comdwleeid@naver.comsjgceo@naver.com
JUNGGYO SEO
Affiliation:
Seoul Science High School, Uamgil 63 (Hyewha-dong 1-1), Jongro-ku, Seoul 110-530, Korea email bjh7790@naver.comyoonhoim@nate.comdwleeid@naver.comsjgceo@naver.com
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Abstract

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It is well known to be impossible to trisect an arbitrary angle and duplicate an arbitrary cube by a ruler and a compass. On the other hand, it is known from ancient times that these constructions can be performed when the use of several conic curves is allowed. In this paper, we prove that any point constructible from conics can be constructed using a ruler and a compass, together with a single fixed nondegenerate conic different from a circle.

Type
Research Article
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

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